frequency distribution scoresfrequency classes/intervals – determined after finding range of data....
TRANSCRIPT
DAY 3
STATISTICS AND DATA ANALYSIS
Frequency DistributionScores Frequency
Classes/Intervals – • Determined after finding range of data.• Class width is the range of each class/interval.
Rule of thumb – 5 to 10All must be equal
• Classes/Intervals are read as follows:60 ≤ x < 7070 ≤ x < 8080 ≤ x < 9090 ≤ x < 100
• Class limits – the upper and lower value in each interval: 60, 70, 80, 90, & 100
• Class marks – midpoint of the classes:65, 75, 85, 95
Frequency – The number of times the score occurred in the data set.
Relative Frequency – The ratio of data within the class to all the data.
Cumulative Frequency – The sum of the frequency for a particular class and all previous classes.
Cumulative Relative Frequency – The ratio of the cumulative frequency of a class to all the data.
63 65 69 64 66 62
66 64 67 70 75 73
72 74 77 79 78 71
76 81 89 87 86 84
83 85 88 82 88 87
87 95 93 99
total
frequency
total
freqcumm ..
60-70
70-80
80-90
90-100
9
10
12
3
Frequency Distribution
Scores Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency60-70 9
70-80 10
80-90 12
90-100 3
26.034
9
56.034
19
91.034
31
0.134
34
26.034
9
29.034
10
35.034
12
09.034
3
Relative Frequency The ratio of data within the class to all the data.
total
frequency
Cumulative Frequency The sum of the frequency for a
particular class and all previous classes.
Cumulative Relative Frequency
The ratio of the cumulative frequency
of a class to all the data.
total
freqcumm ..
9
1931
34
Frequency Distribution Histograms
Create 4 histograms: for frequency, relative frequency, cumulative frequency, and cumulative relative frequency. Scores will be on x-axis, frequencies on y-axis.
Scores
60-70
70-80
80-90
90-100
2
6
8
10
12
4
Frequency
Score
60-70
70-80
80-90
90-100
.10
.30
.40
.50
.60
.20
RelativeFrequency
Score
60-70
70-80
80-90
90-100
5
15
20
25
30
10
CumulativeFrequency
Score
60-70
70-80
80-90
90-100
.2
.6
.8
1.0
.4
CumulativeRelative
Frequency
Score
ScoresScores
Scores35
Frequency DistributionScores Frequency Relative
FrequencyCumulative Frequency
Cumulative Relative
Frequency60-70 9 9
70-80 10 19
80-90 12 31
90-100 3 34
26.034
9
56.034
19
91.034
31
0.134
34
26.034
9
29.034
10
35.034
12
09.034
3
Create 4 histograms: for frequency, relative frequency, cumulative frequency, and cumulative relative frequency. Scores will be on x-axis, frequencies on y-axis.
Scores
60-70
70-80
80-90
90-100
2
6
8
10
12
4
Freq
uenc
y
Score
60-70
70-80
80-90
90-100
.10
.30
.40
.50
.60
.20
Rela
tive
Freq
uenc
y
Score
60-70
70-80
80-90
90-100
5
15
20
25
30
10
Cum
ulati
ve F
requ
ency
Score
60-70
70-80
80-90
90-100
.2
.6
.8
1.0
.4
Cum
ulati
ve R
elati
ve F
requ
ency
Score
ScoresScores
Scores35
Frequency Distribution
Scores Frequency
60-70 |||| ||||
70-80 |||| ||||
80-90 |||| |||| ||
90-100 |||
63 65 69 64 66 62
66 64 67 70 75 73
72 74 77 79 78 71
76 81 89 87 86 84
83 85 88 82 88 87
87 95 93 99
A dot plot is one way to show the frequencies graphically. Simply place a dot to represent each piece of data above the corresponding class/interval.
| | | |60-70 70-80 80-90 90-100
A tally chart is another way to show the frequencies. Simply place a line to represent each piece of data next to the corresponding class/interval.
PRACTICE
Frequency Distributions
25 20 18 26 42 3438 56 29 30 30 40
50 28 21 38 19 20
18 18
Ages of volunteers at a hospital.
Ages Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency
10-20
20-30
30-40
40-50
50-60
4
75
2
2
Total = 20
2.020
4
55.020
11
25.020
5
1.020
2
1.020
2
4
16
11
18
20 0.120
20
35.020
7
9.020
18
8.020
16
2.020
4
Frequency Distribution HistogramsCreate 4 histograms: for frequency, relative frequency, cumulative frequency, and
cumulative relative frequency. Scores will be on x-axis, frequencies on y-axis.
Ages
10-20
20-30
30-40
40-50
2
6
8
10
12
4
Frequency
Age
.10
.30
.40
.50
.60
.20
RelativeFrequency
Age
4
12
16
20
24
8
CumulativeFrequency
Age
.2
.6
.8
1.0
.4
CumulativeRelative
Frequency
Age
AgesAges
Ages28
50-60
10-20
20-30
30-40
40-50
50-60
10-20
20-30
30-40
40-50
50-60
10-20
20-30
30-40
40-50
50-60
Ages of volunteers at a hospital.
Frequency Distributions7.5 8 9.5 9 9 105 7 5.5 6 10 9.5
7 8.5 2 8 9.5 9
7.5 5 3.5 6.5 8 10
Quiz scores – represents entire class.
Scores Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency
1-3
3-5
5-7
7-9
9-11
1
15
8
9
Total = 24
04.024
1
04.024
1
21.024
5
33.024
8
38.024
9
1
27
15
24
04.024
1
08.024
2
29.024
7
63.024
15
0.124
24
Frequency Distribution HistogramsCreate 4 histograms: for frequency, relative frequency, cumulative frequency, and
cumulative relative frequency. Scores will be on x-axis, frequencies on y-axis.
Scores
1-3 3-5 5-7 7-9
2
6
8
10
12
4
Frequency
Score
.10
.30
.40
.50
.60
.20
RelativeFrequency
Score
4
12
16
20
24
8
CumulativeFrequency
Score
.2
.6
.8
1.0
.4
CumulativeRelative
Frequency
Score
ScoresScores
Scores28
9-11
Quiz Scores
1-3 3-5 5-7 7-9 9-11 1-3 3-5 5-7 7-9 9-11 1-3 3-5 5-7 7-9 9-11
Frequency Distributions60 61 62 66 81 6860 66 72 72 63 68
70 71 60 77 66 65
Height in inches – represents a sample of students from a particular school.
Height Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency
60-65
65-70
70-75
75-80
80-85
6
6
4
11
Total = 18
33.018
6
33.018
6
22.018
4
06.018
1
06.018
1
6
12
16
1817
33.018
6
67.018
12
89.018
16
94.018
17
0.118
18
Frequency Distribution HistogramsCreate 4 histograms: for frequency, relative frequency, cumulative frequency, and
cumulative relative frequency. Scores will be on x-axis, frequencies on y-axis.
Height
60-65
65-70
70-75
75-80
2
6
8
10
12
4
Frequency
Height
.10
.30
.40
.50
.60
.20
RelativeFrequency
Height
4
12
16
20
24
8
CumulativeFrequency
Height
.2
.6
.8
1.0
.4
CumulativeRelative
Frequency
Height
HeightHeight
Height28
80-85
Height
60-65
65-70
70-75
75-80
80-85
60-65
65-70
70-75
75-80
80-85
60-65
65-70
70-75
75-80
80-85